Quantitative Stability/flexibility Relationships Research Articles

Revealing the Mechanism of Binding Selectivity in Undecaprenyl Diphosphate Synthase

Undecaprenyl Pyrophosphate Synthase (UPPS) represents an excellent drug target to combat bacterial virulence because it disrupts the glycan biosynthesis pathway when inhibited. Binding of a substrate causes the activity in UPPS from different species to respond differently, making it potentially possible to develop a suite of narrow-spectrum antibiotics. Here, we investigate the differential effects of protein dynamics on the mechanism of action in different species by performing a comparative analysis over the UPPS superfamily, Cis-Isoprenyl Pyrophosphate Synthase (Cis-IPPS) using protein dynamics and pharmacophore modeling. We used MOE and Ligand Scout to compute protein structure and ligand-based pharmacophore models of 14 UPPS protein structures. Molecular dynamics simulation and an ensemble-based statistical mechanics model are used to quantify mobility and stability of UPPS in the apo form, and with bound substrates. We find that quantitative stability flexibility relationships (QSFR) identify conserved flexibly correlated motifs. We find that the binding event affects backbone flexibility over an extended range, suggesting a mechanism of allostery. The most conserved regions in the QSFR motifs include the active site and hydrophobic tunnel, which reflects evolutionary conservation. However, variations are substantial at the interface, particularly in the coiled-coil arm that glues the two monomers together. Interestingly, we observe slight differences in structure-based pharamacophore features across species. We corroborate results obtained from evolutionary trees, pharmacophore modeling, characterization of dynamics and stability to reveal the mechanism of binding selectively. With 14 proteins studied in detail thus far, our results suggest a critical flexibly correlated motion spans both domains of the UPPS homodimer, which creates an allosteric pathway responsible for modulating binding selectively.

Rigidity Emerges during Antibody Evolution in Three Distinct Antibody Systems: Evidence from QSFR Analysis of Fab Fragments.

The effects of somatic mutations that transform polyspecific germline (GL) antibodies to affinity mature (AM) antibodies with monospecificity are compared among three GL-AM Fab pairs. In particular, changes in conformational flexibility are assessed using a Distance Constraint Model (DCM). We have previously established that the DCM can be robustly applied across a series of antibody fragments (VL to Fab), and subsequently, the DCM was combined with molecular dynamics (MD) simulations to similarly characterize five thermostabilizing scFv mutants. The DCM is an ensemble based statistical mechanical approach that accounts for enthalpy/entropy compensation due to network rigidity, which has been quite successful in elucidating conformational flexibility and Quantitative Stability/Flexibility Relationships (QSFR) in proteins. Applied to three disparate antibody systems changes in QSFR quantities indicate that the VH domain is typically rigidified, whereas the VL domain and CDR L2 loop become more flexible during affinity maturation. The increase in CDR H3 loop rigidity is consistent with other studies in the literature. The redistribution of conformational flexibility is largely controlled by nonspecific changes in the H-bond network, although certain Arg to Asp salt bridges create highly localized rigidity increases. Taken together, these results reveal an intricate flexibility/rigidity response that accompanies affinity maturation.

Flexibility Correlation between Active Site Regions Is Conserved across Four AmpC β-Lactamase Enzymes.

β-lactamases are bacterial enzymes that confer resistance to β-lactam antibiotics, such as penicillins and cephalosporins. There are four classes of β-lactamase enzymes, each with characteristic sequence and structure properties. Enzymes from class A are the most common and have been well characterized across the family; however, less is known about how physicochemical properties vary across the C and D families. In this report, we compare the dynamical properties of four AmpC (class C) β-lactamases using our distance constraint model (DCM). The DCM reliably predicts thermodynamic and mechanical properties in an integrated way. As a consequence, quantitative stability/flexibility relationships (QSFR) can be determined and compared across the whole family. The DCM calculates a large number of QSFR metrics. Perhaps the most useful is the flexibility index (FI), which quantifies flexibility along the enzyme backbone. As typically observed in other systems, FI is well conserved across the four AmpC enzymes. Cooperativity correlation (CC), which quantifies intramolecular couplings within structure, is rarely conserved across protein families; however, it is in AmpC. In particular, the bulk of each structure is composed of a large rigid cluster, punctuated by three flexibly correlated regions located at the active site. These regions include several catalytic residues and the Ω-loop. This evolutionary conservation combined with active their site location strongly suggests that these coupled dynamical modes are important for proper functioning of the enzyme.

Mos1 Transposase Thermodynamic Stability and Flexibility

DNA transposons are mobile DNA elements that can move (or transpose) from one DNA molecule to another and thereby deliver genetic information into human chromosomes in order to confer a new function or replace a defective gene. This process is catalyzed by a transposase enzyme. The reaction of transposition occurs in several steps, during which two or more transposase enzymes bind to the terminal inverted repeats on the transposon DNA, bring them together to form a synaptic complex, excise the gene flanked by the terminal inverted repeats, and catalyze strand transfer to insert the excised gene at a new location. Thus, transposases must be sufficiently flexible to allow conformational rearrangements of their domains to bind the transposon DNA and to supply a catalytic site during each step of transposition. Here, we investigate the dynamics, thermodynamic stability, and flexibility of Mos1 transposase, a member of the Tc1/mariner family of transposases. We use a computational model called the minimum Distance Constraint Model (mDCM) and the analysis of quantitative stability/flexibility relationships (QSFR). With these tools, we determine the free energy landscape and the flexibility and mechanical coupling of secondary structure elements or residues in Mos1. Our data provide an insight into how Mos1 is structured and how it functions and are applicable to Tc1/mariner transposases in general.

Thermodynamic Stability and Flexibility Characteristics of Antibody Fragment Complexes

Free energy landscapes, backbone flexibility and residue-residue couplings for being co-rigid or co-flexible are calculated from the minimal Distance Constraint Model (mDCM) on an exploratory dataset consisting of VL, scFv and Fab antibody fragments. Experimental heat capacity curves are reproduced markedly well, and an analysis of quantitative stability/flexibility relationships (QSFR) is applied to a representative VL domain and several complexes in the scFv and Fab forms. Global flexibility in the denatured ensemble typically decreases in the larger complexes due to domain-domain interfaces. Slight decreases in global flexibility also occur in the native state of the larger fragments, but with a concurrent large increase in correlated flexibility. Typically, a VL fragment has more co-rigid residue pairs when isolated compared to the scFv and Fab forms, where correlated flexibility appears upon complex formation. This context dependence on residue- residue couplings in the VL domain across length scales of a complex is consistent with the evolutionary hypothesis of antibody maturation. In comparing two scFv mutants with similar thermodynamic stability, local and long-ranged changes in backbone flexibility are observed. In the case of anti-p24 HIV-1 Fab, a variety of QSFR metrics were found to be atypical, which includes comparatively greater co-flexibility in the VH domain and less co-flexibility in the VL domain. Interestingly, this fragment is the only example of a polyspecific antibody in our dataset. Finally, the mDCM method is extended to cases where thermodynamic data is incomplete, enabling high throughput QSFR studies on large numbers of antibody fragments and their complexes.

Is Rigidity Conserved Across the Class A Beta-Lactamase Family?

Antibiotic overuse has resulted in an evolved class of β-lactamase (BL) proteins that can hydrolyze extended spectrum antibiotics. BL, produced by bacteria, hydrolyzes the β-lactam ring of penicillin and chemically related structures, thus rendering the antibiotic ineffective. NMR and MD results suggest that the TEM-1 class A BL structure is quite rigid. In this study, we characterize flexibility of 15 related Class A BL proteins, which includes several extended spectrum antibiotic resistance. We employ a Distance Constraint Model (DCM). The DCM is a computational modeling scheme that integrates thermodynamic and mechanical descriptions to compute Quantitative Stability/Flexibility Relationships (QSFR) of protein structure [1, 2]. QSFR results suggest that rigidity is constant throughout the BL Class A family, although many site-specific differences in flexibility and rigidity are also present. Interestingly, our results show appreciable diversity within the Ω-loop, which is important for substrate recognition and catalysis. We will attempt to correlate differences in active-site dynamics with antibiotic resistance. Taken together, our collective results provide a biophysical framework to characterize evolution within the class A BL family.[1] Jacobs, D.J., and Dallakyan, S. Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity. Biophys. J, 2005. 88: p. 903-15.[2] Livesay, D.R., Dallakyan, S., Wood, G.G. and Jacobs, D.J. A flexible approach for understanding protein stability. FEBS Lett, 2004. 576: p. 468-67.

Elucidating the Effects of Mutation upon C-Type Lysozyme through Quantitative Stability/Flexibility Relationships

The Distance Constraint Model (DCM) [1, 2] is a computational modeling scheme that integrates thermodynamic and mechanical descriptions to compute Quantitative Stability/Flexibility Relationships (QSFR) of protein structure. We have previously employed the mDCM to predict melting temperatures of c-type lysozyme mutants with a maximum error of 4.3% [3]. Going further, we now assess the differences in other QSFR quantities across the dataset. The model is parameterized by fitting to experimental heat capacity curves. Subsequently, a large number of mechanical descriptions of protein flexibility are calculated. Pronounced changes in rigidity and flexibility at sites remote from the mutation are common. Drastic changes occur in the backbone flexibility at the mutation site and neighboring residues within 6Å. Increases in rigidity and flexibility are nearly equal, and collectively occur more than sites without change. Interestingly, the β-domain becomes flexible in all cases, likely leading to domain unfolding related to aggregation [4]. We also present changes in pairwise residue-to-residue couplings that can affect functional collective motions. [1] Jacobs, D.J., and Dallakyan, S. Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity. Biophys. J, 2005. 88: p. 903-15. [2] Livesay, D.R., Dallakyan, S., Wood, G.G. and Jacobs, D.J. A flexible approach for understanding protein stability. FEBS Lett, 2004. 576: p. 468-67. [3] Verma, D., Jacobs, D.J. and Livesay, D.R. Predicting the melting point of human c-type lysozyme mutants. Current Protein and Peptide Science, 2010, In press. [4] Canet, D., Last, A.M., Tito, P., Sunde, M., Spencer, A., Archer, D.B., Redfield, C., Robinson, C.V. and Dobson, C.M. Local cooperativity in the unfolding of an amyloidogenic variant of human lysozyme. Nature Structure Biology 9, 2002, 308-315.

Towards Comprehensive Analysis of Protein Family Quantitative Stability/flexibility Relationships

The Distance Constraint Model (DCM) is a computational modeling scheme that uniquely integrates thermodynamic and mechanical descriptions of protein structure. As such, quantitative stability/flexibility relationships (QSFR) can be computed. Using comparative QSFR analyses, we have previously investigated the give-and-take between thermodynamics and mechanics across a small number of protein orthologs, ranging from 2 to 9 [1-3]. However, a comprehensive protein family analysis requires consideration of hundreds of proteins. Consequently, homology models are necessary to fill in the structural gaps. As a first step towards such comprehensive analyses, herein we assess the differences within QSFR quantities calculated from the human c-type lysozyme x-ray crystal structure and homology models constructed from various orthologs. We parameterize our current minimal DCM (mDCM) by fitting to experimental Cp curves. All models are able to reproduce the experimental Cp curve. Interestingly, the least squares fitting error is not correlated to homology model accuracy. We present quantitative differences within various QSFR metrics between the x-ray and model structures, and establish thresholds on model accuracy based on their ability to reproduce the QSFR metrics of the x-ray structure. [1] Livesay and Jacobs (2006). Proteins, 62: 130-143. [2] Livesay et al. (2008). Chem Central J, 2:17. [3] Mottonen et al. (2009). Proteins, 75:610-627.

Unifying mechanical and thermodynamic descriptions across the thioredoxin protein family

We compare various predicted mechanical and thermodynamic properties of nine oxidized thioredoxins (TRX) using a Distance Constraint Model (DCM). The DCM is based on a nonadditive free energy decomposition scheme, where entropic contributions are determined from rigidity and flexibility of structure based on distance constraints. We perform averages over an ensemble of constraint topologies to calculate several thermodynamic and mechanical response functions that together yield quantitative stability/flexibility relationships (QSFR). Applied to the TRX protein family, QSFR metrics display a rich variety of similarities and differences. In particular, backbone flexibility is well conserved across the family, whereas cooperativity correlation describing mechanical and thermodynamic couplings between the residue pairs exhibit distinctive features that readily standout. The diversity in predicted QSFR metrics that describe cooperativity correlation between pairs of residues is largely explained by a global flexibility order parameter describing the amount of intrinsic flexibility within the protein. A free energy landscape is calculated as a function of the flexibility order parameter, and key values are determined where the native-state, transition-state, and unfolded-state are located. Another key value identifies a mechanical transition where the global nature of the protein changes from flexible to rigid. The key values of the flexibility order parameter help characterize how mechanical and thermodynamic response is linked. Variation in QSFR metrics and key characteristics of global flexibility are related to the native state X-ray crystal structure primarily through the hydrogen bond network. Furthermore, comparison of three TRX redox pairs reveals differences in thermodynamic response (i.e., relative melting point) and mechanical properties (i.e., backbone flexibility and cooperativity correlation) that are consistent with experimental data on thermal stabilities and NMR dynamical profiles. The results taken together demonstrate that small-scale structural variations are amplified into discernible global differences by propagating mechanical couplings through the H-bond network.

Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family

BackgroundGram-negative bacteria use periplasmic-binding proteins (bPBP) to transport nutrients through the periplasm. Despite immense diversity within the recognized substrates, all members of the family share a common fold that includes two domains that are separated by a conserved hinge. The hinge allows the protein to cycle between open (apo) and closed (ligated) conformations. Conformational changes within the proteins depend on a complex interplay of mechanical and thermodynamic response, which is manifested as an increase in thermal stability and decrease of flexibility upon ligand binding.ResultsWe use a distance constraint model (DCM) to quantify the give and take between thermodynamic stability and mechanical flexibility across the bPBP family. Quantitative stability/flexibility relationships (QSFR) are readily evaluated because the DCM links mechanical and thermodynamic properties. We have previously demonstrated that QSFR is moderately conserved across a mesophilic/thermophilic RNase H pair, whereas the observed variance indicated that different enthalpy-entropy mechanisms allow similar mechanical response at their respective melting temperatures. Our predictions of heat capacity and free energy show marked diversity across the bPBP family. While backbone flexibility metrics are mostly conserved, cooperativity correlation (long-range couplings) also demonstrate considerable amount of variation. Upon ligand removal, heat capacity, melting point, and mechanical rigidity are, as expected, lowered. Nevertheless, significant differences are found in molecular cooperativity correlations that can be explained by the detailed nature of the hydrogen bond network.ConclusionNon-trivial mechanical and thermodynamic variation across the family is explained by differences within the underlying H-bond networks. The mechanism is simple; variation within the H-bond networks result in altered mechanical linkage properties that directly affect intrinsic flexibility. Moreover, varying numbers of H-bonds and their strengths control the likelihood for energetic fluctuations as H-bonds break and reform, thus directly affecting thermodynamic properties. Consequently, these results demonstrate how unexpected large differences, especially within cooperativity correlation, emerge from subtle differences within the underlying H-bond network. This inference is consistent with well-known results that show allosteric response within a family generally varies significantly. Identifying the hydrogen bond network as a critical determining factor for these large variances may lead to new methods that can predict such effects.

Conserved quantitative stability/flexibility relationships (QSFR) in an orthologous RNase H pair

Many reports qualitatively describe conserved stability and flexibility profiles across protein families, but biophysical modeling schemes have not been available to robustly quantify both. Here we investigate an orthologous RNase H pair by using a minimal distance constraint model (DCM). The DCM is an all atom microscopic model [Jacobs and Dallakyan, Biophys J 2005;88(2):903-915] that accurately reproduces heat capacity measurements [Livesay et al., FEBS Lett 2004;576(3):468-476], and is unique in its ability to harmoniously calculate thermodynamic stability and flexibility in practical computing times. Consequently, quantified stability/flexibility relationships (QSFR) can be determined using the DCM. For the first time, a comparative QSFR analysis is performed, serving as a paradigm study to illustrate the utility of a QSFR analysis for elucidating evolutionarily conserved stability and flexibility profiles. Despite global conservation of QSFR profiles, distinct enthalpy-entropy compensation mechanisms are identified between the RNase H pair. In both cases, local flexibility metrics parallel H/D exchange experiments by correctly identifying the folding core and several flexible regions. Remarkably, at appropriately shifted temperatures (e.g., melting temperature), these differences lead to a global conservation in Landau free energy landscapes, which directly relate thermodynamic stability to global flexibility. Using ensemble-based sampling within free energy basins, rigidly, and flexibly correlated regions are quantified through cooperativity correlation plots. Five conserved flexible regions are identified within the structures of the orthologous pair. Evolutionary conservation of these flexibly correlated regions is strongly suggestive of their catalytic importance. Conclusions made herein are demonstrated to be robust with respect to the DCM parameterization.

A flexible approach for understanding protein stability

A distance constraint model (DCM) is presented that identifies flexible regions within protein structure consistent with specified thermodynamic condition. The DCM is based on a rigorous free energy decomposition scheme representing structure as fluctuating constraint topologies. Entropy non-additivity is problematic for naive decompositions, limiting the success of heat capacity predictions. The DCM resolves non-additivity by summing over independent entropic components determined by an efficient network-rigidity algorithm. A minimal 3-parameter DCM is demonstrated to accurately reproduce experimental heat capacity curves. Free energy landscapes and quantitative stability-flexibility relationships are obtained in terms of global flexibility. Several connections to experiment are made.